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Thread: Lipschitz continuous

  1. September 3rd 2011, 10:08 AM #1
    Camille91
    Camille91 is offline
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    Lipschitz continuous

    Assume f: [0, 2\pi] \rightarrow \mathbb{R} is Lipschitz continuous. Prove that exists constans C>0 that for every k=1,2... there is:
    \int^{2\pi}_{0} f(x) \sin (kx) dx \leq \frac{C}{k}.
    Last edited by Camille91; September 3rd 2011 at 11:33 AM.
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